DANIEL JUSTENS
90 articles published in Tangente
Math for everyoneN°226Oct 07, 2025The false mysteries of graphical proofs in mathematics
Discover how seemingly rigorous diagrams can fool us: the missing square paradox, the astonishing proof that every triangle is equilateral, and more.
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History and CultureN°91Aug 26, 2024How Cauchy saw the world
In a series of lectures, Cauchy reveals his vision of the real world through the science of his day. They reveal a scholar wrestling with his religious convictions.
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Math for everyoneN°91Aug 25, 2024A distribution like no other
Standard probability distributions can sometimes be far removed from what is observed. When extreme cases occur too often, the Cauchy distribution comes into its own.
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History and CultureN°218Jun 13, 2024Beyond the Gaussian curve in finance
Gaussian curves are unsuitable for modelling risky financial assets such as stocks. To overcome this problem, Benoît Mandelbrot introduced the concept of a multifractal measure and generalized Brownian motion.
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Math for everyoneN°89Feb 16, 2024Fractions and music: when 3/4 is not equivalent to 6/8
Octaves, fifths, triplets… The rhythms and pitches of Western music were built on fractions.
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Math for everyoneN°215Jan 14, 2024Bridge: a bridge between games and statistics
Bridge begins with an auction, in which players commit to taking a minimum number of tricks during play. Statistical methods make it possible to rationalize this decision-making process.
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KnowledgeN°88Nov 21, 2023The first law of large numbers
Repeating a random experiment with two possible outcomes a large number of times leads to probabilities that are difficult to predict directly, let alone calculate explicitly. Yet the de Moivre–Laplace theorem provides an excellent approximation.
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Math for everyoneN°88Nov 21, 2023The first law of large numbers
Repeating a random experiment with two possible outcomes a large number of times leads to probabilities that are difficult to predict directly, let alone calculate explicitly. Yet the de Moivre–Laplace theorem provides an excellent approximation.
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Math for everyoneN°88Nov 20, 2023The brilliant insight that black holes exist
The finite speed of light and its particle nature led Laplace, through a bold line of reasoning, to contemplate the existence of black holes—before changing his mind. Although he could not have conceived of light's dual nature at the time, he was right!
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Math for everyoneN°87Aug 24, 2023In probability: the Bienaymé–Chebyshev inequality
Summarizing a set of observations with a few key numbers is essential. But how much do these numbers tell us about the frequencies within particular intervals? The Bienaymé–Chebyshev inequality provides a first quantitative answer.
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History and CultureN°87Aug 24, 2023The birth of thermodynamics
The study of heat transformed our view of the world by prompting us to consider whether a physical "arrow of time" exists. It all comes down to one remarkably simple relation: the Clausius inequality.
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Math for everyoneN°87Aug 24, 2023Chebyshev and monotone sequences
Elementary results can sometimes prove astonishingly fertile, opening the way to a host of developments and applications. Chebyshev's inequality is a case in point.
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